The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function
@article{Berg2007TheFP, title={The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function}, author={Christian Berg and Antonio J. Dur'an}, journal={Mathematica Scandinavica}, year={2007}, volume={103}, pages={11-39} }
We study the fixed point for a non-linear transformation in the set of Hausdorffmoment sequences,
defined by the formula: T ((an))n = 1/(a0+�E �E �E+an).We determine the corresponding measure�E,
which has an increasing and convex density on ]0, 1[, and we study some analytic functions related
to it. TheMellin transform F of �E extends to ameromorphic function in the whole complex plane.
It can be characterized in analogy with the Gamma function as the unique log-convex function
on ].1…
Figures from this paper
16 Citations
On a fixed point in the metric space of normalized Hausdorff moment sequences
- Mathematics
- 2010
We show that the transformation (x_n)_{n\ge 1}\to (1/(1+x_1+...+x_n))_{n\ge 1} of the compact set of sequences (x_n)_{n\ge 1} of numbers from the unit interval [0,1] has a unique fixed point, which…
On an Iteration Leading to a q-Analogue of the Digamma Function
- Mathematics
- 2013
We show that the q-Digamma function ψq for 0<q<1 appears in an iteration studied by Berg and Durán. This is connected with the determination of the probability measure νq on the unit interval with…
On Markov Moment Problem and Related Results
- MathematicsSymmetry
- 2021
New results and theorems on the vector-valued Markov moment problem are proved by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result.
From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications
- Mathematics
- 2020
The aim of this review paper is to recall known solutions for two Markov moment problems, which can be formulated as Hahn–Banach extension theorems, in order to emphasize their relationship with the…
On Markov Moment Problem and Mazur-Orlicz Theorem
- Mathematics
- 2017
Applications of the generalization of Mazur-Orlicz theorem to concrete spaces are proved. Suitable moment problems are solved, as applications of extension theorems of linear operators with a convex…
On truncated and full classical Markov moment problems
- Mathematics
- 2021
Abstract Giving necessary and sufficient conditions for the existence of solutions of truncated and full classical Markov moment problems in terms of the given (or measured) moments, in Lp,μ (S) (1 ≤…
Moment problems and orthogonal polynomials
- Mathematics
- 2011
In 1894 Thomas Jan Stieltjes (1856-1894) published an extremely influential paper: Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse, 8, 1–122; 9, 5–47. He introduced what is now known…
Moment Problems on Bounded and Unbounded Domains
- Mathematics
- 2013
Using approximation results, we characterize the existence of the solution for a two-dimensional moment problem in the first quadrant, in terms of quadratic forms, similar to the one-dimensional…
On the Moment Problem and Related Problems
- MathematicsMathematics
- 2021
Firstly, we recall the classical moment problem and some basic results related to it. By its formulation, this is an inverse problem: being given a sequence (yj)j∈ℕn of real numbers and a closed…
References
SHOWING 1-10 OF 25 REFERENCES
A transformation from Hausdorff to Stieltjes moment sequences
- Mathematics
- 2004
We introduce a non-linear injective transformation τ from the set of non-vanishing normalized Hausdorff moment sequences to the set of normalized Stieltjes moment sequences by the formulaT[(an)n=1∞]n…
The Markov moment problem and de Finetti’s theorem: Part I
- Mathematics
- 2004
Abstract.The Markov moment problem is to characterize sequences admitting the representation sn=∫01xnf(x)dx, where f(x) is a probability density on [0,1] and 0≤f(x)≤c for almost all x. There are…
Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers
- MathematicsCanadian Journal of Mathematics
- 2005
Abstract We introduce some non-linear transformations from the set of Hausdorff moment sequences into itself; among them is the one defined by the formula: $T\left( {{\left( {{a}_{n}} \right)}_{n}}…
On Powers of Stieltjes Moment Sequences, I
- Mathematics
- 2005
For a Bernstein function f the sequence sn=f(1)·...· f(n) is a Stieltjes moment sequence with the property that all powers snc,c>0 are again Stieltjes moment sequences. We prove that
$$s_n^c$$ is…
Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
- Mathematics
- 1984
1 Introduction to Locally Convex Topological Vector Spaces and Dual Pairs.- 1. Locally Convex Vector Spaces.- 2. Hahn-Banach Theorems.- 3. Dual Pairs.- Notes and Remarks.- 2 Radon Measures and…
Monotone Matrix Functions and Analytic Continuation
- Mathematics
- 1974
I. Preliminaries.- II. Pick Functions.- III. Pick Matrices and Loewner Determinants.- IV. Fatou Theorems.- V. The Spectral Theorem.- VI. One-Dimensional Perturbations.- VII. Monotone Matrix…
Potential Theory on Locally Compact Abelian Groups
- Mathematics
- 1975
I. Harmonic Analysis.- 1. Notation and Preliminaries.- 2. Some Basic Results From Harmonic Analysis.- 3. Positive Definite Functions.- 4. Fourier Transformation of Positive Definite Measures.- 5.…
The Gamma Function
- Mathematics
- 1964
In what follows, we introduce the classical Gamma function in Sect. 2.1. It is essentially understood to be a generalized factorial. However, there are many further applications, e.g., as part of…
Regular Variation in R k
- Mathematics
- 1988
Researchers investigating certain limit theorems in probability have discovered a multivariable analogue to Karamata's theory of regularly varying functions. The method uses elements of real analysis…